Valuations and Dynamics of Negotiations

Abstract

This paper analyzes three-party negotiations in the presence of externalities, deriving a close form solution for the stationary subgame perfect Nash equilibrium of a standard non-cooperative bargaining model. Players' values are monotonically increasing (or decreasing) in the amount of negative (or positive) externalities that they impose on others. Moreover, players' values are continuous and piecewise linear on the worth of bilateral coalitions, and are inextricably related to their negotiation strategies: the equilibrium value is the Nash bargaining solution when no bilateral coalitions form; the Shapley value when all bilateral coalitions form; or the nucleolus, when either one bilateral coalition among `natural partners' or two bilateral coalitions including a `pivotal player' form.

Keywords: Coalitional bargaining, externalities, value, negotiations.

JEL Classification: C71, C72, C78, D62.